Sample size for testing homogeneity of two a priori dependent binomial populations using the Bayesian approach.
Sampling inference, Bayes' inference and robustness in the advancement of learning.
Scientific learning is seen as an iterative process employing Criticism and Estimation. Sampling theory use of predictive distributions for model criticism is examined and also the implications for significance tests and the theory of precise measurement. Normal theory examples and ridge estimates are considered. Predictive checking functions for transformation, serial correlation, and bad values are reviewed as is their relation with Bayesian options. Robustness is seen from a Bayesian view point...
Scaling of model approximation errors and expected entropy distances
We compute the expected value of the Kullback-Leibler divergence of various fundamental statistical models with respect to Dirichlet priors. For the uniform prior, the expected divergence of any model containing the uniform distribution is bounded by a constant . For the models that we consider this bound is approached as the cardinality of the sample space tends to infinity, if the model dimension remains relatively small. For Dirichlet priors with reasonable concentration parameters the expected...
Sequential classification in the case of many populations
Sequential estimation of survival functions with a neutral to the right process prior
In this work, a parametric sequential estimation method of survival functions is proposed in the Bayesian nonparametric context when neutral to the right processes are used. It is proved that the mentioned method is an 1-SLA rule when Dirichlet processes are used; furthermore, asymptotically pointwise optimal procedures are obtained. Finally, an example is given.
Simultaneous minimax estimation of parameters of multinomial distribution
The problem of minimax estimation of parameters of multinomial distribution is considered for a loss function being the sum of the losses of the statisticians taking part in the estimation process.
Some Applications of Anderson's Inequality to Some Optimality Criteria of the Generalized Least Squares Estimator.
Some problems of prediction of the difference of random variables
Spiked Dirichlet process priors for Gaussian process models.
Stability and conditional Γ-minimaxity in Bayesian inference
Two concepts of optimality corresponding to Bayesian robust analysis are considered: conditional Γ-minimaxity and stability. Conditions for coincidence of optimal decisions of both kinds are stated.
Stable-1/2 bridges and insurance
We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions for the...
Statistical analysis of periodic autoregression
Methods for estimating parameters and testing hypotheses in a periodic autoregression are investigated in the paper. The parameters of the model are supposed to be random variables with a vague prior density. The innovation process can have either constant or periodically changing variances. Theoretical results are demonstrated on two simulated series and on two sets of real data.
Stochastic algorithm for Bayesian mixture effect template estimation
The estimation of probabilistic deformable template models in computer vision or of probabilistic atlases in Computational Anatomy are core issues in both fields. A first coherent statistical framework where the geometrical variability is modelled as a hidden random variable has been given by [S. Allassonnière et al., J. Roy. Stat. Soc.69 (2007) 3–29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models. A consistent stochastic algorithm has been introduced...
Subjective Bayesian Multivariate Stratified Sampling From Finite Populations.